You couldn't fail to have goose pimples, sitting in Westminster Hall watching a tiny, stocky yet far from frail old lady walk in wearing a vivid canary costume, accompanied by a taller, older man with that slightly mocking smile that always seems to hover about the duke's lips.

Maybe it was the cold that affected our skin – it's always freezing in Westminster Hall, even in high summer – but it might also have been the images called to mind: the memories of a very pretty but nervous young woman who came to the throne, unexpectedly, at a time when there was still rationing, almost every British city was studded with bomb sites, beer cost a shilling a pint, few people had television and needed to draw the curtains to watch it; when every film ended with the national anthem and she was even made to watch the cup final.

So we were in Flummeryworld, that theme park where the British are so happy and at ease. Attending such an event is like being wrapped in velvet and tucked into a presentation box. Westminster Hall is the oldest public building in Britain, and probably Europe. It was packed. I spotted several leftwing Labour MPs, for even in parliament if you scratch a republican you will often find a quivering royalist.

Trumpeters of the Household Cavalry were lined up under the great stained glass to the south of the hall, like the world's poshest window cleaners. The band of the Scots Guards played Fantasia on Greensleeves.

Various processions arrived, swirling about, including doorkeepers, serjeants at arms (actual and deputy), the clerk of the crown in chancery (Sir Suma Chakrabarti KCB), trainbearers, chaplains, the gentleman usher of the black rod, plus the lord speaker, an ancient title that goes back all of six years. In Flummeryworld there must be constant renewal, like the rides at Disneyland.

Beefeaters, or "the Queen's body guard of the yeomen of the guard" – for the most part elderly grizzled men – arrived in their Tudor costumes, with their pikes. It was like being inside a Ladybird book on the glorious pageant of our island history.

Then we heard the traditional sound of walkie-talkies squawking outside the door, as anxious officials awaited the presence. The royal couple walked in a few feet from the media seats. We could have shouted "break a leg, your majesty!" but happily no one did.

Next the speeches. The lord speaker from the House of Lords – in Flummeryworld, the peers are still the more important house – used the language unrolled for such occasions. Lady D'Souza praised her "stewardship". She was grateful because parliament had been "granted the privilege" of being "the first of Your people formally to honour Your jubilee". In the text of her speech, even the royal pronoun had a capital letter, and somehow the baroness managed to pronounce it.

She mentioned the new stained glass window, which was a present paid for by MPs and lords (will any of them try to get their contribution on expenses?). "Your Coat of Arms and Royal Cypher will bathe the Hall in colour."

She ended with a flourish, which might have been trumpeted rather than merely spoken. "Your Majesty, the lords spiritual and temporal in parliament assembled give thanks for this, your diamond jubilee. We look forward to the years to come and we pray that you and your realms may enjoy the peace, plenty and prosperity that have so distinguished your reign!"

John Bercow, the Commons speaker, was slightly lighter (the Queen had been on the throne for almost 11 years before he was born). But he recalled rationing when it meant more than just waiting for the latest iPad. He praised the way she had helped hold the nation together when it "could have been torn asunder" – asunder being one of those flummery words never used in real life.

Then he said, slightly alarmingly, that she was a "kaleidoscope Queen". What did this mean? That if you picked her up and shook her, she'd look different? It turned out to be something to do with change and variety.

He slipped into a cascade of the letter S. The jubilee would be full of moments "striking for the sincerity expressed as much for the scenery encountered. Sixty years of stability, 60 years of security, 60 years of sacrifice, 60 years of service." The applause was long and, I think, genuine.

Then it was her (sorry, Her) turn to reply, in that voice as familiar to us as our own childhood. She was "reassured" that she was only the second British monarch even to have had a diamond jubilee. "I have had the pleasurable duty of treating with 12 prime ministers" and there was laughter, as there always is at royal humour – though perhaps tinged with relief that she didn't add: "Mind you, there wasn't much pleasurable about treating with Ted Heath. Or Gordon Brown."

Over such a period, she thought, "one can observe that venerable old age can be a guide but not a prerequisite for success in public office" – another slight ripple of amusement. And there was praise for Prince Philip, "who is well-known for declining compliments of any kind".

Then, after barely 20 minutes, it was over. The royal party and the costumed characters from Flummeryworld went off together for drinks and nibbles, and the rest of us emerged blinking into the real, workaday world, which just happened to be washed in bright sunlight.

Elizabeth II addresses both Houses of Parliament – and former prime ministers – in Westminster and gets her first look at a new stained glass window, commissioned to mark her 60th year on the throne and paid for by subscriptions from MPs and members of the House of Lords